The Mongols, like many other empires that had their origin in the steppe, got their start by causing much destruction along the territories they conquered. And just like other Steppe empires they spent their reign rebuilding what they first destroyed. The Mongols nurtured (creation implying too much action) growth to something greater than even they managed to destroy. The Silk Road flourished mightily under the patronage of the Mongols. Officials could traverse up to 400 KM a day using the high way that developed. This highway was open to private individuals, although they didn't have the ability to get new horses from the stations along its way. Establishment sprung up to cater to this traffic in eastern China. The entire highway ran from both sides of the Empire. Paper money was introduced on a large skill to promote trade.

To provision northern China of supplies Kubilia commissioned a grand canal to be built. Building it required over 2million workers. It's important to stress continuity, and China had been becoming increasingly commercialised since the period of division that followed the collapse of the Tang. Here the Mongol era can be seen as the continuation of previously existing trends.

Cultural cross pollination of Eurasia under the Mongols had major influence on everybody involved. The old Mongol capital of qaraqorum was built using the best that the Afro-Eurasian cultural sphere had to offer. Afro-Eurasian cultural sphere because of course not everybody involved in the empire belonged to it. Marco Polo was one such individual. A Venetian who spent years in the Mongol court and may even have administered a large Chinese city for a while.

The Mongol Empire initially had a very detrimental impact on the economies of Eastern Europe, the Middle East, Central Asia and China, particularly during its rapid establishment and expansion under Genghis Khan. The Mongols did well as they secured resources and slaves from the cities they pillaged, but that destruction did significant harm to regional economies. Persia and China under the rule of Mongol successors flourished in time, but if anything, this was a recovery. Other areas weren't so resilient. For instance, Marco Polo and other explorers of the time often avoided Central Asia - previously a main thoroughfare for transcontinental trade - and traversed the Eurasian continent largely by other routes.

Central Asia before the Mongol invasion was experiencing the height of human accomplishment up to that point in areas such as urban planning, commerce, medicine, science and others. The Mongols would uproot much of this. Primary sources from Central Asian scholars and others attest to a common practice of exterminating the inhabitants of conquered cities - such as Termez - and even other living creatures. With such significant loss (or displacement) of life and property, trade, commerce and much of society collapsed in those areas. Northern China and Eastern Europe would have similar experiences. The Mongols' effect on Eastern Europe would materialize in the form of the so-called Mongol-Tatar Yoke, contributing to the disintegration of Kievan Rus' - the premier political entity of Eastern Europe at the time - and putting in place a tribute system that would help stunt East European states. Parts of the Middle East - particularly Baghdad and other parts of Iraq - arguably would not return to a comparable level of population or development until the twentieth century.

The Mongol Empire unified Europe and Asia in a way that had never been done before. This certainly contributed to the exchange of ideas, but that was often through displacement and it was an incredibly destructive process - one of the most destructive in human history. It's also suspected that was how the Black Death was transmitted to Europe, so even the exchanges themselves weren't always beneficial . . . In terms of (very) long-term effects, this is the point at which Central Asia starts losing its status as a center of intellectual and economic activity, and the Russian Empire would eventually fill the void.

I'm getting most of this from Dan Carlin's Wrath of the Khans podcast and Lost Enlightenment by S. Frederick Starr. I'm guessing it's a messier answer than you were hoping for, but hopefully it gives you some more talking points and makes your presentation more interesting. It's popular to focus on a simple story of unification and prosperity - and the Silk Road definitely happened - but the Mongols slaughtered millions of people along its land routes first, while others benefitted. If you're still looking to piece this together, I'd start with some Wikipedia articles and radiate out into authoritative sources from there.